# Design of Experiments 1 and 2

Design of Experiments 1A baseball player would like to conduct an experiment to determine how the weight of his bat, the speed of a pitch and the type of pitch affect the distance he can hit the ball in the air. The player will examine two different bat weights (32 ounces or 35 ounces), three pitch speeds (70, 80 or 90 miles per hour) and two types of pitch (fastball or curveball). Pitches will be thrown by a pitching machine to guarantee consistency. The baseball player will hit 15 balls using each of the factor level combinations, and the distance (in feet) that each ball travels before hitting the ground will be recorded.1. Identify the following in this experiment:(a) experimental units(b) response variable(c) factors(d) factor levels(e) treatments(f) How should randomization be used in this experiment? Explain why this randomization is important.(g) Suppose that one of the treatments results in the baseball player consistently hitting the ball farther than for the other treatments. Can we say that the treatment is the cause? Explain.Design of Experiments 2A cereal manufacturer is trying to increase sales of one of its breakfast cereals. The marketing director plans to conduct an experiment to investigate the effect of the colour of the cereal box and the shelf placement on the sales of the cereal. A total of 360 grocery stores in North America that carry this cereal are available for the study. For each store, the colour of the box (red, blue or yellow) and the shelf placement (top, middle or bottom shelf) will be randomly determined. Total sales will be compared at the end of a three-month period. The marketing director believes results may vary between Canada and the U.S., so the experiment is conducted separately for the 120 Canadian stores and the 240 American stores.(a) What type of experiment is this? Identify the following in this experiment:(b) experimental units(c) response variable(d) factors(e) factor levels(f) treatments(g) Is there a blocking variable in this experiment? If so, what is it?(h) How is the principle of control used in this experiment?(i) How is the principle of repetition used in this experiment?Matched Pairs ExperimentsWe would like to conduct an experiment to determine whether university students can text faster than they can type on the computer. Subjects will be given a paragraph to type. The same paragraph will be used whether it is being typed on a cell phone or on a computer. There are 25 volunteers available for the study.1. Explain how a matched pairs experiment should be conducted to compare texting and typing speeds. Be sure to explain the role of randomization, and why it is important in this experiment.Sampling SchemesThe NHLPA is a union representing all National Hockey League players. The union is conducting a survey to gauge players’ opinions about a proposed change in the league’s salary structure.For each of the following proposed sampling schemes, identify (i) the type of sample that is obtained and (ii) any bias in the way the sample is chosen.*Note: When conducting a survey by phone, by mail or even in person, there is always the possibility that someone will refuse to respond. This cannot be avoided, even using proper sampling techniques. For part (ii) of each question, only describe the potential bias (if any) introduced by the way the sample is selected.(a) A random sample of five players from each of the league’s 30 teams is selected. These selected players are contacted by a union representative.(b) The survey is sent to all players in the league. Players are asked to respond by email.(c) The survey is distributed to players attending an NHLPA meeting in New York.(d) A random sample of seven NHL teams is selected. Ten players from each of these ten teams are randomly selected and are contacted by telephone to respond to the survey.(e) Two hundred players are randomly selected from a list of all NHL players. Union representatives administer the survey in person to each of the selected players.(f) The survey is posted on the NHLPA’s private website. Players are invited to email their comments to a union representative.